document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082182>Question 1082182</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7^7+36<BR>\n" );
document.write( "Whats is the prime factor of this number?<BR>\n" );
document.write( "It is 43*107*179<BR>\n" );
document.write( "But how can find this without calcuator? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696447 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=696447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "When it comes to prime factorization, there are very few shortcuts and one is generally stuck using an algorithm to find all the factors.  \r<BR>\n" );
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document.write( "For this problem, one thing you could do is look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E7+=+823543+ ALIGN=MIDDLE  ALT=\"7%5E7+=+823543+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and look at the remainder when dividing by the various prime numbers:\r<BR>\n" );
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document.write( "    7^7 mod 43 = 7   ==>  43 (= 7 + 36) divides evenly into (7^7 + 36)\r<BR>\n" );
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document.write( "Once you know that, however, you need to divide 823543 by 43 to get 19153.  Then you must continue to check this for divisibility by prime numbers (up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%2819153%29+ ALIGN=MIDDLE  ALT=\"+sqrt%2819153%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 138.39) to try to factor this part.\r<BR>\n" );
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document.write( "19153/2  no (clearly!)<BR>\n" );
document.write( "19153/3  no<BR>\n" );
document.write( "19153/5  no<BR>\n" );
document.write( "19153/7  no<BR>\n" );
document.write( "19153/11 no<BR>\n" );
document.write( "...<BR>\n" );
document.write( "19153/107  yes!   its 179   (179 is also prime so the task is complete at this step).\r<BR>\n" );
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document.write( "So we found 43, 107, and 179  divide evenly into  7^7+36.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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